The matrix \(\mathbf {A(\mathit {c})}\) , describes
affine lattice transformations using hexagonal symmetry as the reference
structure [1]}, [2]}.
With \(c=0\) , the transformation matrix is an identity matrix and Eq.
REF  describes a hexagonal symmetry in 2D [3]}.
In the current work, we choose the hexagonal and square symmetries
to represent phases with compositions \(c=0\)  and \(c=1\)  respectively.
These symmetries are chosen to illustrate exaggerated symmetry deformations
during phase transition. The transformation coefficients in Eq. REF ,
\((X=\alpha ,\beta ,\theta )\) , are modeled as linear functions of the
dimensionless composition field, \(X(c)=X_{0}+c\Delta X\) . We define
\(X_{0}\)  to be the transformation coefficients corresponding to the
hexagonal lattice \((\alpha _{0}=\beta _{0}=1,\theta _{0}=\frac{\pi }{3})\) ,
and \(\Delta X\)  is the deformation required to transform the lattice
with a hexagonal symmetry to a square symmetry \((\Delta \alpha =\Delta \beta =0,\Delta \theta =\frac{\pi }{6})\) .
Note, in both the hexagonal and square lattice symmetries, the transformation
matrix encourages a periodic lattic- symmetry spacing of \(\frac{4\pi }{q_{0}\sqrt{3}}\) . 
